Not sure if this is possible, but if so I would like very much know how to accomplish the following.

Allowing a customer to place an order at any given time by accessing Odoo ofcourse limited access.

Thanks in advance.

Edit: odoo 9 (latest deb file, does not have this feature as it seems), So removed 9 version, installed git clone of odoo 8. And now I do have this feature. Works on ubuntu wily (15.10). jquery.blockUI.js problem resolved by replacing it with latest version

User can add order, or purchase. But using our suppliers as option to buy. Instead it be necessary to place order internally (sort of) client places order with us. Not with our suppliers. (select supplier option, is not something I would like my customers to see)

W.r.t your query, I have gone through it and tried to replicate it.
Few recommendations which I would like to suggest you which might
cater to your needs are as follows:-

1) Yes its possible to allow a customer to place an order at any
given time by granting them access rights.

2) The configuration which you need to follow is that by Signing
Up an external user. This can be done by
Settings>Configuration>General Setting>Portal
Access>Allow external users to sign up

3) After doing so we need to the login page and SignUp
ourselves with inputs required.

4) Now once you log in with the user (the one which you had signed
up), you will see that no menus are visible to the user(s).

5)
For this we need to login with admin and go
to Settings>Users>Users>Select the user
created>Related Partner>Sales and Purchases>Customers.
By selecting Customer
in the last step we
have made sure that the User created is a Customer

6) Also we need to configure the Access Rights under Settingsso as to make the menus visible to the User as required.